\prob{4}
The magnitude of the Earth's gravitational force on a point mass is F(r), where r is the distance from the Earth's center to the point mass. Assume the Earth is a homogenous sphere of radius R.

What is

32

8

4

2

1

Mechanics}Gravitational Law

Recall the famous inverse square law determined almost half a millennium ago,

where .

The ratio of two inverse-square forces (, where is the radius of the planet or huge heavy object) would be

Thus, , which is choice (C).

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Don't you have to take into account that the mass is not concentrated at the center? where = M / (4/3)R^3 you get a mass of M/8 then take into account the radial contribution of 4 to get a final answer of 1/2. Where'd i go wrong?